Self-Consistent Direct Method for Chemical Abundances in High-z Galaxies with JWST

TL;DR

This work introduces a self-consistent direct method to determine the physical conditions of high-ionization gas in $z>5$ galaxies by jointly using OIII] $1661,1666$ and [OIII] $\lambda4363$, $\lambda5007$ diagnostics. By combining $T_{\rm e}$–$n_{\rm e}$ intersections with Monte Carlo and MCMC forward modeling, the authors derive $n_{\rm e}$ and $T_{\rm e}$ for the O$^{2+}$ zone, and compute O/H and N/O from ionic abundances, finding $n_{\rm e}$ up to $3\times10^{5}$ cm$^{-3}$ and $T_{\rm e}$ near $2\times10^{4}$ K for $z>6$, with metallicities moving upward by up to $\sim$0.29 dex relative to previous estimates. They show that high-density corrections substantially affect the MZR at high redshift and can alleviate some of the reported N/O anomalies, though NIV]–based N$^{3+}$ diagnostics are highly temperature-sensitive and may overestimate N/O if $T_{\rm e}$ varies between zones. The paper emphasizes the critical role of density and temperature structure, the uncertainties in ICFs, and the need for larger, diverse JWST samples and improved atomic data to robustly map chemical evolution in the early universe.

Abstract

The unprecedented rest-frame UV and optical coverage provided by JWST enables simultaneous constraints on the electron density (n$_{\rm e}$) and temperature (T$_{\rm e}$) of ionized gas in galaxies at z>5. We present a self-consistent direct method based on multiple OIII]1661,66) and [OIII] ($λ$4363, and $λ$5007) transitions to characterize the physical conditions of the high-ionization zone. This new approach is insensitive to a wide range of n$_{\rm e}$ due to the high critical densities of the OIII] and [OIII] transitions. Applying this technique to six galaxies at z=5-9, we find electron densities up to n$_{\rm e}$$\sim 3\times 10^{5}$ cm$^{-3}$ and temperatures of T$_{\rm e}$ $\sim 20,000$ K in systems at $z>6$. Accounting for these self-consistent densities changes the derived T$_{\rm e}$ and modifies the inferred metallicities by up to 0.29 dex relative to previous estimates. We discuss the reported N/O overabundances in the high-$z$ galaxies from our sample, which arise entirely from the high N$^{3+}$/H$^{+}$ values inferred from NIV] lines. We point out that a T$_{\rm e}$-stratification, in which the N$^{3+}$ zone has a slightly higher T$_{\rm e}$ than T$_{\rm e}$([OIII]), could substantially reduce the inferred N/O. Quantitatively, if T$_{\rm e}$(N$^{3+}$) were 10\% higher than T$_{\rm e}$([OIII]), this could induce a systematic overestimation of N$^{3+}$/O$^{2+}$ of nearly 50\%. Classical N/O diagnostics such as N$^{+}$/O$^{+}$, due to their critical densities, can significantly impact the inferred N/O abundance in the presence of high-density gas, whereas N$^{2+}$/O$^{2+}$ place these galaxies closer to $z\sim0$ systems in the N/O-O/H plane. Future JWST programs with larger and more diverse samples will be essential to test the universality and robustness of these results.

Figures (6)

• Figure 1: The $T_{\rm e}$vs.$n_{\rm e}$ diagnostics based on the reported O iii] $\lambda 1666$ and [O iii] $\lambda \lambda 4363, 5007$ fluxes and their associated uncertainties for the sample of high-$z$ galaxies listed in Table \ref{['tab:oiii_properties']}. The most likely combination of $n_{\rm e}$ and $T_{\rm e}$ for the high-ionization gas is indicated by the intersection of the diagnostic curves. When the errors are small, the combination of these diagnostics provide a self-consistent approach to derive $T_{\rm e}$([O iii]) and $n_{\rm e}$([O iii]). The density values previously adopted to determine $T_{\rm e}$([O iii]) are indicated by the red vertical line, with a shaded band representing the uncertainty estimated by the reference authors. In the case of RXCJ2248-ID-T24, topping24a only stated that a density of $1\times 10^{5}$ cm$^{-3}$ was assumed, without providing a clear associated uncertainty range.
• Figure 2: The mass–metallicity relation (MZR) for galaxies at $z=5$–$9$. Metallicity estimates derived in this study using the self-consistent method for $T_{\rm e}$([O iii]) and $n_{\rm e}$([O iii]) are plotted in different symbols in colour-coded with $n_{\rm e}$, while those compiled from the original studies are shown with the same symbols in gray topping24atopping25aarellanocordova25curti25amarqueschaves:24Berg25b. For RXCJ2248-ID-T24 and A1703-zd6 the metallicities obtained here are 0.18–0.29 dex higher than the values reported in the original works (see also Table \ref{['tab:oiii_properties']}). For RXCJ2248-ID3-B25, we inferred a O/H 0.25 lower that in the original result. For comparison, different MZR determinations across various redshifts with metallicities estimated using strong-line methods are shown as lines : curti20, curti24a, and nakajima23, stanton25b ($z = 4-8$), and Berg22 using the $T_{\rm e}$-sensitive method.
• Figure 3: The N/O–O/H relation for galaxies at $z > 5$ is shown using different symbols. Black symbols correspond to the original abundance ratios reported by the reference authors, which exhibit signatures of nitrogen enrichment at $12 + \log(\mathrm{O/H}) < 8.0$topping24atopping25aarellanocordova25marqueschaves:24Berg25b. The N/O ratios reported in Berg25b correspond to values obtained without applying an ICF correction (see Sec. \ref{['sec:disc']}). For reference, local star-forming regions from the DESIRED project MendezDelgado:23besteban25, with abundances determined via the direct method, are shown as gray circles. The O/H and N/O, (N$^{2+}$/O$^{2+}$) and (N$^{2+}$ + N$^{3+}$)/O$^{2+}$), re-derived using our self-consistent procedure described in Sec. \ref{['sec:physica_conditions']} are presented as pink (left panel) and orange (right panel) symbols, respectively. For reference, the right panel shows the mean value of $\log(\mathrm{N^{2+}/O^{2+}}) = \log(\mathrm{N/O}) = 1.01 \pm 0.17$, indicated by a dashed line. The revised N/O estimates using N$^{2+}$/O$^{2+}$ for high-$z$ galaxies are consistent with the intrinsic dispersion observed in the local sample, whereas the inclusion of N$^{3+}$ increases the N/O ratio by 0.64 dex relative to the N$^{2+}$/O$^{2+}$ ratio. The dashed line represents the relation of nicholls17 from stellar abundances from the Milky Way. The results of N/O derived using N$^+$/O$^{+}$ and (N$^+$ + N$^{2+}$)/O$^{2+}$) are discussed in Sec. \ref{['sec:disc']}.
• Figure 4: Results for the N$^{+}$/O$^{+}$ ratio as a function of O$^2+$/O$+$, derived using densities of 10$^{3}$ cm$^{-3}$ (squares), 10$^{4}$ cm$^{-3}$ (circles), and $10^{4.7-4.8}$ cm$^{-3}$ (triangles) for RXCJ2248-ID3-T24 (blue) and RXCJ2248-ID3-B25 (orange). The higher densities in this analysis ($10^{4.7-4.8}$ cm$^{-3}$, triangles) correspond to the Si iii] values reported in the original studies of topping24a and Berg25b. The correlation between N$^{+}$/O$^{+}$ and O$^{2+}$/O$^{+}$ arises from the low critical density of [O ii]$\lambda\lambda$3726,29, which leads to an overestimation of O$^{+}$ as the density increases. Note that this illustrative result shows the impact of the variations of N$^{+}$/O$^{+}$ when assuming three different values of the electron density. The inferred N$^{+}$/O$^{+}$ ratios for RXCJ2248-ID-T24 and RXCJ2248-ID3-B25 correspond to the use of $n_{\rm e}$$=10^{4}$ cm$^{-3}$ for low ionization ions as our preferred values. The results in Table \ref{['tab:oiii_properties']} shows the final N$^{+}$/O$^{+}$ ratio inferred as indicated in Sec. \ref{['sec:physica_conditions']} for each galaxy.
• Figure 5: Grotrian diagram Grotrian:28 illustrating the forbidden transitions of O$^{2+}$, generated with PyNebluridiana15.